I experimented with the Inkscape spiral tool (set to divergence = 10) and compared it to a logarithmic spiral generated with The Geometer's Sketchpad. (see image) The two horizontal lines at the bottom are "sliders" to adjust the two constants: k, which controls the rate of expansion of the spiral, and a, which is just a scale factor. I was able to import an image created with Inkscape and superimpose the computed spiral. Interestingly, I was able to get the two curves to match for over a full turn, but then they diverged. No combination of settings for k and a were able to make the curves match in both the inner and outer parts of the curve. This tells me that something is a little strange in the inkscape tool. Perhaps an approximate algorithm is being used that does a piecewise approximation to a logarithmic spiral. I would like to hear from whoever created the tool or anyone else who understands the math used to create it. http://www.nabble.com/file/6223/Clip1.gif
--David Chandler